Donaldson's Theorem is a significant result in the field of differential geometry, particularly concerning the topology of smooth manifolds. It states that certain smooth four-dimensional manifolds can be distinguished by their intersection forms, which are algebraic structures that describe how surfaces intersect within the manifold. This theorem has profound implications for understanding the structure of four-dimensional spaces. The theorem is named after mathematician Simon Donaldson, who introduced it in the 1980s. His work provided new insights into the classification of 4-manifolds and led to the development of Donaldson invariants, which are tools used to study these manifolds' properties.